Mathematics Grade 9 Gauteng November 2016 Question Paper

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Downloaded from hlayiso.com MATHEMATICS 2 GRADE 9 GAUTENG DEPARTMENT OF EDUCATION PROVINCIAL EXAMINATION MATHEMATICS MARKS: 120 TIME: 2 hours INSTRUCTIONS AND INFORMATION 1. This question paper consists of SECTION A and SECTION B based on the prescribed content framework in the CAPS document. SECTION A: QUESTION 1: SECTION B: QUESTION 2: QUESTION 3: QUESTION 4: QUESTION 5: QUESTION 6: QUESTION 7: QUESTION 8: MULTIPLE-CHOICE QUESTIONS Ten multiple-choice questions based on all five content areas Answer this section on the answer sheet provided. SEVEN QUESTIONS BASED ON FIVE CONTENT AREAS Numbers, operations and relations Patterns and algebra Algebra Functions Space and shapes Measurement Data handling 2. Answer ALL questions from both SECTIONS. 3. Anon-programmable calculator may be used unless otherwise stated. 4. In SECTION A, circle the letter of the correct answer. If you change your decision cross out the circled letter and circle your new choice 5. In SECTION B, show all necessary steps in your working unless otherwise stated. 6. | When answering questions, candidates must apply their knowledge, skills and insight. 7. | Number the answers correctly according to the numbering system used in this question paper. 8. Write neatly and legibly. P.T.O.

SECTION A QUESTION 1 Downloaded from hlayiso -com MATHEMATICS GRADE 9 ANSWER THIS QUESTION ON ANSWER SHEET A. Circle the letter of the correct answer from the four possible answers. 1. 1.2 1.3 1.4 Which of the following numbers is a rational number? A B Cc D Joa 0,141141114 Ve 1 Simplify 5,6+ 1,2 x3 A 9,2 B 20,4 Cc 41,6 D 204 The next term in the sequence 1;1;1; 4;1;951;...,is... A 1. B 16. Cc 14. D 10. Complete the statement: The expression G9 AW Pp 2x45 4x4] has nA nN (1) (1) () ... terms. (1) P.T.O.

1.5 1.6 1.7 1.8 The value of x in the figure below is: 9 Aw YP Downloaded from hlayiso.com 124° 38° 56° 94° 90° The value of x is: A B Cc D The volume of the given prism is: Oo Aw YP 70° 110° 30° 55° x, x 5x?cm> 5x?cm? 10x cm? (2x + 5)cm? 142° Scm MATHEMATICS GRADE 9 If the perimeter of a square is 20 cm, then the area of the square is equal to: A B Cc D 400 cm? 25 em? 5m? 100 cm? (1) (1) (1) (1) P.T.O.

Downloaded from hlayiso.com MATHEMATICS 5 GRADE 9 1.9 The median of a set of data is the: A Biggest number — smallest number B Middle number Cc Most common number D Average of the data oo) 1.10 In how many ways can you arrange the four cards side by side as shown below? BEG: A 32 B 24 Cc 16 qd) D 8 [10] SECTION B QUESTION 2 2.1 An amount of R15 000 is invested for 5 years at compound interest of 8% per annum. 2.1.1 What is the total value of the investment after 1 year? (2) 2.1.2 Calculate the total value of the investment after 5 years. (3) 2.2 Calculate /—64+(—3)° without using a calculator. (2) : 3 1 1 . 2.3 A recipe needs 4 cups of sugar, | 3 cups of flour and a 3 cup of milk. Write the ratio of the ingredients in the simplest form. (2) 2.4 A large truck uses 16,5 litres of diesel per 100 kilometres. Calculate how much diesel the truck will need to travel 1 284 km. (3) [12] P.T.O.

Downloaded from hlayiso.com QUESTION 3 3.1 3.2 Is the following statement correct? Show by calculation to prove your answer. MATHEMATICS GRADE 9 Study the pattern below and answer the questions that follow. 5 B 8 Figure 1 Figure 2 a | Figure 3 3.1.1 How many balls must be added to draw the next figure? 3.1.2 Draw and complete the table in your answer book. Figure 1 4 5 Number of balls 5 (@) (2) 3.1.3. Is the general rule 7, =3(n—1)+5 correct to determine the number of balls for any figure in the pattern? Prove your answer by finding the general rule using the table above. (3) (2x-1)? =4x? +1 QUESTION 4 4.1 4.2 4.3 Subtract 4x” —3 from —2(2x” —3x+5) Simplify. 3 421 2 (4p 288 419) 12 6 4x° —2x(3x") 4.2.2 5 2x Factorise fully. x(at+ y)—-(y+a) (2) [8] (3) (3) (3) (2) P.T.O.

Downloaded from hlayiso.com MATHEMATICS GRADE 9 4.4 Solve the following equations. 44.1 2(x+2)-(x-3)=5 (4) 2x 2x 1 44.2 —+——= 5 xt] l-x x?-1 ©) 443 10° =0,0001 (2) 4.5 The sum of three consecutive even numbers is 78. Determine the three numbers. (5) [27] QUESTION 5 5.1 Determine the rule for the following flow diagram. x y 4 -9 -/-—_. _ -3.0 -—> -——> | -7 5 | I 9 (2) 5.2 Calculate the gradient of a line through the points (0 ; 0) and (-2 ; -3). 4 4 3 2 4 1 > 3-2 1 2 3 -2 (-2 ; -3) -3 -4 (2) 5.3. The equation y—1=2(x-—2) defines a straight line graph. 5.3.1 Write down the y-intercept of the graph. qd) 5.3.2 Calculate the x-intercept of the graph. (3) 5.3.3 Draw the graph in your answer book. (2) P.T.O.

Downloaded from hlayiso.com MATHEMATICS GRADE 9 5.4 Study the graph below and answer the questions that follow. y 5.4.1 Which of the two graphs, p or s has a positive gradient? Explain. 5.4.2. The equation of pis y=x+2.If p 1s andthe y— intercept of s is the point (0 ; 5), determine the equation of s. (2) (2) [14] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 9 GRADE 9 QUESTION 6 6.1 Determine with reasons, the sizes of angles a and b in the diagram below. a b 55° (4) 6.2 AB=BE and BF = FD. Prove that DC = BE. B Cc IN2 F 1 I 2 A , D E (4) 6.3 Study the diagram below and answer the questions that follow. A B 3cm . C 5,2 cm 4cm ~ 2N E 7,50m D 6.3.1 Prove that AAED /// ADCB. (6) 6.3.2 Hence, find the length of AD. (4) P.T.O.

Downloaded from hlayiso.com MATHEMATICS 10 GRADE 9 6.4 Draw the image of A S after a rotation of 90° anticlockwise about the origin O (0; 0). Use ANSWER SHEET B to answer this question. “\ Ls \ Zz (3) [21] QUESTION 7 7.1 Study the prism below and answer the questions that follow. B 3m AD 7m E 4m F 7.1.1 Find the length of BC. (4) 7.1.2 Draw the net of the prism in your answer book. d) 7.1.3 Calculate the surface area of the prism. (3) P.T.O.

Downloaded from hlayiso.com MATHEMATICS "1 GRADE 9 7.2. A field, 480 000 m? is 160 m wide. What length of fencing is needed to fence it? 2 480 000 m’ 160 m x (4) 7.3 Arectangular fish tank with an open top is shown below. +m — 700cm ——— > 300 nf 4 sookm 7.3.1 Calculate the volume of the tank. (2) 7.3.2 How many litres of water do we need to fill the tank? (2) [16] QUESTION 8 8.1 A set of data below are marks obtained by Grade 9 learners in one of their Mathematics tests. The test was out of 50 marks. 4, 12,16,8,16,24,32,12,24,36,48, 16,32, 48 8.1.1 Calculate the mean and median of the data. (3) 8.1.2 What is the mode? Qd) 8.1.3 Calculate the range. qd) P.T.O.

Downloaded from hlayiso.com MATHEMATICS 12 GRADE 9 8.2 The chart below represents Sipho’s daily activities after school from Monday to Friday of each week. He has seven hours daily to run all these activities. Sipho’s after school activity schedule 14% « Extra Maths lesson: 28% « Sports: 29% * Homework: 29% « TV: 14% 29% 29% 8.2.1 On which activity does he spend the most of his time? How many hours does he spend on this activity? (2) 8.2.2 On which activity does he spend the least time? How many hours does he spend on this activity? (2) 8.3. Two red, one white and three blue marbles are put into a bag. If you put your hand once into the bag without looking and pull out one marble, what is the probability of: 8.3.1 Pulling out a blue marble? (2) 8.3.2 Not pulling out a white marble? qd) [12] TOTAL: 120 END

Downloaded from hlayiso.com FORMULA SHEET MATHEMATICS 13 GRADE 9 Simple Interest: Compound Interest: l= Prn ~ 100 A=P(1+i)" A=P(1+in) r A=P(1+—)" ( 100 A=P(1+—~) 100 Perimeter Area Square 4(l) 1? Rectangle 2(1+b) lxb Circle 2ur mr? il Triangle (sl+s2+s3) 3P xLh Parallelogram 2(b+1) bxLh 1 =(a+b)xXLh Trapezium Sum of the 4 sides 2 a and b = parallel lines Rhombus 4l bX1Lh 1 2(a+b) * x did, Kite 2 a and b = length of equal sides d, and d, = diagonals

Downloaded from hlayiso.com MATHEMATICS 14 GRADE 9 ANSWER SHEET A Name: Grade: 9 SECTION A Marks: 10 Circle the letter of the correct answer. Submit this with your answer book. Question Answer 1.1 A C D 1.2 A C D 1.3 A Cc D 1.4 A C D 1.5 A C D 1.6 A Cc D 1.7 A Cc D 1.8 A C D 1.9 A Cc D 1.10 A Cc D

Downloaded from hlayiso.com MATHEMATICS 15 GRADE 9 ANSWER SHEET B NAME: GRADE: 9 QUESTION 6.4 ond

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